L.E.J. Brouwer, A Mathematician on Self

Luitzen Egbertus Jan Brouwer (1881-1966) was
a Dutch mathematician who emerged from academic obscurity to briefly challenge
the scientific community of his day with a new theory of the foundation of
mathematics that he called "Intuitionism." Unlike most thinkers whose ideas
develop over the course of their career, Brouwer's ideas seemed to have matured
early: in an adolescent "Profession of Faith" and in a lengthy essay composed
when he was still a graduate student title "Life, Art, and Mysticism." The
subject of the essay was unusual for a budding mathematician, but Brouwer was
uniquely fascinated by philosophical issues. The work is a youthful apologia for
solitude and the solitary life. The work remained the sentimental grounding for
Brouwer's Intuitionism and was an inspiration to him throughout his life.

Biography

The life of Brouwer is easily summarized. His upbringing was
entirely uneventful. He was an excellent student and quickly progressed through
university studies. He married in 1904. As a graduate mathematics student in
1905, Brouwer composed "Life, Art, and Mysticism." About this time he also
bought a plot of land in the forest outside of a Bohemian village (Laren)
favored by artists and progressive thinkers, located some 20 miles from
Amsterdam. A friend designed the cottage and Brouwer called it "de Hut." Here he
worked on his 1097 doctoral dissertation (titled "On the Foundations of
Mathematics") and would retreat the rest of his life to do his best work.

For
five years, Brouwer addressed the field of topology in a flurry of lectures and
over 40 scholarly articles. He became the foremost authority on topology in the
Netherlands, culminating in appointment to a University of Amsterdam
professorship. From this platform he launched his controversial Intuitionism,
not only attacking the formalism of the mathematical thinking of his day but also
proposing new and insightful views on set theory and negation.

As with most
brilliant but unrelenting personalities, Brouwer provoked rivalries and enemies,
so that by 1928 he was denied by the university all but mundane teaching (versus editorships,
committees, conference travel, etc.). He spent the rest of his life in
relative silence, seeking out occasional lectureships in Germany and Britain. He wrote to
a friend:

All my life's work has been wrested from me and I am left in fear, shame, and
mistrust, and suffering the persecution of my baiting torturers.

Brouwer's last years were spent in what commentator Stigt calls "social
isolation." He was killed as a pedestrian by a car when he was 85 years old.

Art, Life, and Mysticism

The circumstances surrounding Brouwer's "Art, Life,
and Mysticism" reveal much about his personality. Brouwer had just graduated,
and in the Fall of 1904, an arch-Hegelian professor named Bolland had assumed the chair of
philosophy at Leiden University. Bolland's pompous and arrogant views
provoked
young Brouwer into publicly responding to Bolland in a student magazine. Then
Brouwer was invited to offer public comments in Delft, for which he composed
lectures that became "Life, Art and Mysticism," printed in March 1905.

Stigt calls the essay "the ideological manifesto of one of the greatest
mathematical philosophers of this [twentieth] century." "Life, Art, and
Mysticism" is arranged into nine chapters:

The Sad World

Turning into Oneself

Man's Downfall Caused by the Intellect

Atonement

Language

Immanent Truth

Transcendent Truth

The Freed Life

Economics

1.

Chapter one opens with a reflection on how Brouwer's native Holland
exists in the unnatural state of a perpetual "self-imposed burden," that of
shoring itself against the sea. This duty is a living symbol of human
decline from a simple and free state of natural existence. Brouwer offers
this bit of postulated anthropology:

Originally man lived in isolation, supported by nature. Every
individual sought to maintain his equilibrium between sinful temptations.
This filled the whole of his life. There was no involvement with others ,
nor was there any worry about the future. As a result hard work did not
exist, nor did sorrow, hatred, fear, or lust.

But the balance was lost when some desired control over others, a cascade
of force, oppression, conspiracy, and consolidation of power.

We have now reached the point where everyone has power but at the same
time suffers oppression. The old instinct of separation and isolation now
lives only as pale envy and jealousy.

Brouwer quotes Meister Eckhart on how every person confuses acting and
knowing, living for self-made illusions while insisting on knowledge and
truth. By understanding is meant overthrowing and destroying and turning
things upside down.

2.

The remedy to this chaos is simply put: "Look within yourself." At first
there is resistance and inertia but the successful result of looking within
is control of passions, the falling away of plurality and a sense of "joyful
quiescence." Again, Brouwer quotes Eckhart and adds passages from the German
mystic Jakob Boehme:

It is within you. If only you can be silent for one hour and forget all
your desires and feelings, you will hear the unspeakable words of God.

When you are silent you are like God before the formed nature and
creatures, including yours. You will then hear and see with what God saw
and heard in you before your own willing, seeing, and hearing had begun.

From this complex field of the mind, its images and presentiments, the
self finds context for understanding the world. The mind recognizes free will, causality and direction for self, contentment and equanimity.
Looking at the "sad world," one feels thereafter a "pointless
dissatisfaction."

3.

In this section Brouwer develops the notion of intellect as the source of
human captivity to desire and fear. The intellect links desire and image,
object and passion, in a revolving and deepening circle of folly. As the
intellect applies itself to society and culture, the circle of desire and
fear widen to encompass greater human activity beyond the needs of physical
nature. Most nefarious in this collective sphere is manufacturing,
technology, and science, transforming the individual into a sickly
cog.

In reaction to the cycle of desire and fear, the intellect emerges as
conscience, with intimations of happiness and nostalgia for a lost paradise.
An individual must be moved by conscience to seek out something higher, but
the regimen of society, labor, industry, and duty assure that such pangs of
conscience will be well muted. Religion becomes a captive institution, and
even art is controlled -- even those with potential to change the prevailing
system.

Whoever plays a part in the mechanism of society and so helps to
maintain its evil mass production are kept quiet and happy. In books and
drama they are told about reformers, revolutionaries, and recluses, about
contempt for law and order, self-denial, freely-chosen poverty and hunger,
the free life, the Kingdom of God. Such people and their teachers are
greatly admired, at least when presented in writings or on the stage: but
when they appear in real life everyone is outraged and frightened, and they
are locked up in prison or a lunatic asylum.

Brouwer repeats that conscience knows better if it can resist the corrupt
world, that "every now and then conscience breaks away from the bonds of the
sad world," discovering and admiring, especially when one is young, the
purity of "dreamers, monks, and hermits."

4.

Brouwer briefly describes how the corruption of the world easily
reabsorbs the average individual into its prescribed ways:

You will be reconciled with your world and not try to change it. You will
work, eat, sleep, and travel in your world, knowing it to be your inevitable
karma.

5.

Brower explores language as the companion of intellect and the prescribed
social form of communication. Language channels the cycle of fear and desire
into specific nuances and cross-purposes. Conversation is the intellect's
great mask, concealing instincts and feelings in order to establish norms to
control social parameters and behavior. But Brouwer argues these conclusions
from anecdote and literary example, less than effective, and in a tone of
disaffection.

6.

Lingering discontent with the order and values of human society reveal
"irruptions of truth." Here truth is sensed but not articulated; it is
"immanent truth." It guides, enlightens, makes the nature of life and the
world clearer. We see hints of immanent truths in art, for example, which
"belies common sense, causality, and science everywhere."

To transcend worldly views, art must first be free of individual
temperament -- where the created object is merely ingratiated with the
superficialities of the world. Secondly, art must transcend historical
materialism, wherein the created object is an intentional agent of the
world. Brouwer criticizes comedy as a deliberate optimism that plays upon
exaggeration and appearance. He criticizes tragedy as a deliberate
accommodation to cruelty and fate. The visual arts are static, he claims,
outside of time, offering greater potential for insight.

Brouwer digresses to a discussion of women that is characteristically
misogynistic, representing his mindset and that of his era. Women are seen
as shifting between tempestuous sirens and mere distractions (to men). Their passion
is "free from the illusion of space" and their bodies and temperaments
suited to patience and longevity of mind. Brouwer resents the notion of
women's equality, linking the social role of women with the social
degeneration of institutions and industry of the time. He sees the role of
men as the actors and thinkers. Even negatively as "sins of male activity,"
women will inevitably inherit in a future equality a worse fate than the
present fate to which women are doomed to "menial, ignoble tasks." If men's love for
women is a "sad, blind passion," then a woman's love for a man is blindness.

These passages are particularly ungrateful and uncharitable aspects of
Brouwer's personality and thought. As translator Stigt points out,
Brouwer had just married a woman older than himself, well-established
financially, and with a thriving business, while he in contrast was
something of a penniless vagabond and a long-time student. A clear alliance
of interests, if not love, propelled their successful and lifelong marriage,
so that these remarks -- never repeated in subsequent writings -- reveal a
passion or resentment in the youthful Brouwer. Such passions have often not
escaped men, whether
contemporary or classical, writing on the subject of women, from St. Jerome
to Friedrich Nietzsche.

7.

While immanent truths are suggested by perception, transcendent truth is
first approached as breaking the dominant cycle of fear and desire. This
negation of reality's harsh foundation suggests delusion and pretext,
the salving of conscience. True enough that transcendent truth will not be
found in the social order, nor in nearly any art, which is reduced to
"titillation in times of prosperity, or ideal endorsement in times of strife
and hardship."

Nor is immanent truth to be found in language, whether of philosophers,
preachers, nor reformers (the latter being, according to Brouwer,
vegetarians, theosophists, and socialists). Here Brower makes exaggerated
attacks on these groups as if they dominated the society, culture,
technology, and power structure that has brought modern culture to its
present plight. Like Plato, Brouwer inveighs against poets as spinners of
falsehood -- and likewise priests, politicians, and painters.

But Brouwer admits that "sometimes only the accompaniment of transcendent
truth may be heard in life" by the humble-minded, even if truth is absent
from that person's perceptions. Those who are "imprisoned in life" will call
these flashes or insights mysticism. Those who understand will realize that
mysticism is not simply a passing phantasm that does not interfere with life
and duty. Rather, mysticism "denies that there is anything positive to be
found in this life," that reality is a "pantheistic world" that envelops and
accommodates transcendent truth.

Such a perception is an "irritation" to authorities. The shortcomings
of Western "semi-mystics" in not developing their perceptions beyond the
standard theological imagery has marked them as heretics on the one hand and
instable and inadequate on the other.

Mysticism denies knowledge, where occultism promotes the intellect's
thirst for it. Mysticism leaves specific issues to rational inquiry, to the
mundane realm of human interaction. Mysticism does not promote
contradictions but transcends them with irrefutable insights that only can
be dismissed but not resolved. Brouwer offers passages from Boehme and the
Bhagavad-Gita to illustrate the nature of mystical expression.

8.

The "freed life" is the life of such insight, but it is not necessarily
different outwardly, except that it will reveal humility, "disregard for
pleasure, property, honor, and work -- except the tasks immediately before
one." "Life will move toward absolute solitude," he writes.

Despite this humility and reticence, others will be uneasy, resentful,
hostile to the point of violence and vengefulness towards that "freed" one.
Such pressure to conform can only be resisted by constantly refreshing the
intellect with the insights of immanent truth. Only this effort will "help
his [the solitary's] patient move away from human society." The burdens of
the body will grow fewer, needs will be eliminated, the environment of the
mind cleansed, the path clearer.

He will go on and reach a state of ever greater solitude, poverty, and
immobility. The last that society will see of him is when he disappears, a
hermit seeking the barren heath over lush but dull vegetation, seeking the
night rather than the insipid light of day. Often he will bathe in the
ocean. He knows that he is destined for even greater poverty.

This is the poverty Meister Eckhart describes: "those who do not want
anything, do not know anything, and do not have anything," as Brower quotes
Eckhart in a long passage. Brouwer returns to the Bhagavad-Gita: "That one
whose delight is but in self, whole pleasure is in self, whose satisfaction
is in self alone, has no work that he must do." Brouwer ends the section
with a colorful passage from Flaubert's Gymnosophists -- and, unfortunately,
more misogynic rants to mar his placid air of self-confidence.

9.

Brouwer excoriates those who work within society for its improvement.
Injustice is intrinsic to society, to the play of power and abuse. Were it
otherwise, society would not exist, would see its institutions and
structures collapse in "self-correction." But Brouwer's attitude here lacks
empathy. While it is true that the masses of humanity will never understand
their self-inflicted misery and never come to any form of enlightenment, Brouwer's
intemperate tone does not reflect a presumed appreciation of
mysticism. Better to tear one's vision away from this sea of suffering and
ignorance, Brouwer pleads -- and that is how he resolves the dilemma in the last possible
paragraphs.

Look at this world, full of wretched people, who imagine that they have
possessions, worried that they might lose them and ever toiling in the hope
of acquiring more. Look at all these people, striving after luxury and
wealth, those whose riches are secured, whose stocks and shares are safely
deposited, and who now nurture an insatiable appetite for knowledge, power,
health, glory and pleasure.

Only he who recognizes that he has nothing, that he cannot possess
anything, that security is unattainable, only he who completely resigns
himself and sacrifices all, who gives everything, who does not know
anything, who does not want anything and does not want to know anything, who
abandons and neglects all, he will receive all. The world of freedom is
opened to him, the world of painless contemplation and -- of nothing.

Conclusion

"Life, Art, and Mysticism" draws its interest as the unexpected work of a
youthful mathematician on the brink of intellectual and soul-searching
discovery. Brouwer never again referred to this essay, though it forever
crafted his philosophy of life and inspired his mathematical work in
challenging logic and method with intuition. Though unrefined and crude in
places, the essay redeems itself as a sweeping gesture in the style of the
time, a heart-felt search for self-understanding and a person's place between
society and solitude.